The final version of the programme (with the list of the accepted abstracts) is available here.

A very wide variety of processes in science, engineering and biology involve evolutionary PDE. Numerical simulations and predictions, particularly for scientific purposes, demand the use of accurate numerical methods for solving systems of time dependent partial differential equations. This is most evident in acoustics, when attempting to evolve weak signals for long distances and for long times or in the simulation of turbulent flow when attempting to capture small structures on relatively coarse grids. In addition to the classical requirement of conservation, of fundamental importance is high accuracy in both space and time for all processes involved (e.g. advection, reaction, diffusion, dispersion). However, as is well-known from Godunov’s theorem, accuracy of linear schemes greater than one brings in the Gibbs phenomenon, producing solutions with spurious oscillations. The real challenge is then to construct non-linear (non-oscillatory) schemes of high accuracy, even for solving linear problems.

Significant advances have been made in the last three decades on the construction of conservative, non-linear schemes of high order of accuracy in both space and time. These advances were pioneered by the family of TVD (Total Variation Diminishing) methods, by now a well-established approach that produces relatively simple and practical second-order schemes. To go beyond second-order, a high degree of sophistication is required. There are at present several approaches that, at least partially, fulfil some of the basic requirements. Examples include the ENO method and its variant the WENO method, the DG Finite Element methods, the ADER approach and the Residual Distribution method.

THEMES OF THE CONFERENCE

Algorithm design, analysis and applications of non-linear schemes of accuracy greater than two, following the finite difference, finite volume or finite element approaches, methods for unsteady problems, multiphase flows, plasma physics, multi-physics  applications, high-order mesh generation.